absolute value - A positive number representing the distance from 0 on a number line

19 decreased by the absolute value of c

19 decreased by the absolute value of c
Take this algebraic expression in parts:
[LIST]
[*]Absolute value of c: |c|
[*]19 decreased by the absolute value of c is found by subtracting |c| from 19
[/LIST]
[B]19 - |c|[/B]

5 -8| -2n|=-75

Subtract 5 from each side:
-8|-2n| = -80
Divide each side by -8
|-2n| = 10
Since this is an absolute value equation, we need to setup two equations:
-2n = 10
-2n = -10
Solving for the first one by dividing each side by -2, we get:
n = -5
Solving for the second one by dividing each side by -2, we get:
n = 5

A researcher posed a null hypothesis that there was no significant difference between boys and girls

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 120 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 6.0. What's the absolute value of the difference between means?
|70 -65| = |5| = 5

Absolute Value

Add, subtract, multiply or divide any two numbers with absolute value signs. Positive Difference.

absolute value of x is less than or equal to 4

absolute value of x is less than or equal to 4
Absolute value of x:
|x|
Set up an inequality where this is less than or equal to 4:
[B]|x| <= 4 [/B] <-- This is our algebraic expression
To solve this, we have the following compound inequality:
-4 < x < 4

Absolute value of x less than 8

Absolute value of x is denoted as |x|.
Set that to less than 8, we have:
|x| < 8

Absolute value of x less than 8

These are now available as shortcuts. You can type any number or variable in the following forms:
[LIST]
[*]Absolute value of x less than 8
[*]Absolute value of x less than or equal to 8
[*]Absolute value of x greater than 8
[*]Absolute value of x greater than or equal to 8
[*]Absolute value of x equal to 8
[/LIST]

Basic Statistics

Given a number set, and an optional probability set, this calculates the following statistical items:

Expected Value

Mean = μ

Variance = σ^{2}

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Expected Value

Mean = μ

Variance = σ

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Complex Number Operations

Given two numbers in complex number notation, this calculator:

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

distance between -2 and 9 on the number line

distance between -2 and 9 on the number line
Distance on the number line is the absolute value of the difference:
D = |9 - -2|
D = |11|
D = [B]11[/B]

Equation and Inequalities

Solves an equation or inequality with 1 unknown variable and no exponents as well as certain absolute value equations and inequalities such as |x|=c and |ax| = c where a and c are constants. Solves square root, cube root, and other root equations in the form ax^2=c, ax^2 + b = c. Also solves radical equations in the form asqrt(bx) = c. Also solves open sentences and it will solve one step problems and two step equations. 2 step equations and one step equations and multi step equations

Express the fact that x differs from 3 by less than 2/7 as an inequality involving absolute value. S

Express the fact that x differs from 3 by less than 2/7 as an inequality involving absolute value. Solve for x.
Let's build this algebraic expression in pieces:
The phrase [I]differs from[/I] means a difference.
x - 3
By less than 2/7 means we use the < sign compared to 2/7
x - 3 < 2/7
Finally, the problem says we involve absolute value. So we write this as:
[B]|x - 3| < 2/7[/B]

Find all numbers whose absolute value is -3

Find all numbers whose absolute value is -3
[B][U][I]None[/I][/U][/B]. Absolute values are always positive, so no number has a negative absolute value.

Find all numbers whose absolute value is 6

Find all numbers whose absolute value is 6.
2 numbers:
|6| = 6
|-6| = 6

find all numbers whose absolute value is 7

find all numbers whose absolute value is 7
|7| = 7
|-7| = 7
So we have two numbers: [B](-7, 7)[/B]

Find all numbers who’s absolute value is 7

Find all numbers who’s absolute value is 7
We have 2 numbers with an absolute value of 7:
[LIST=1]
[*][B]7 [/B]since |7| = 7
[*][B]-7[/B] since |-7| = 7
[/LIST]

Fractions and Mixed Numbers

Given (improper fractions, proper fraction, mixed numbers, or whole numbers), this performs the following operations:

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

Function

Takes various functions (exponential, logarithmic, signum (sign), polynomial, linear with constant of proportionality, constant, absolute value), and classifies them, builds ordered pairs, and finds the y-intercept and x-intercept and domain and range if they exist.

If approximately 68% of the scores lie between 40.7 and 59.9 , then the approximate value of the sta

If approximately 68% of the scores lie between 40.7 and 59.9 , then the approximate value of the standard deviation for the distribution, according to the empirical rule, is
The empirical rule states 68% of the values lie within 1 standard deviation of the mean. The mean is the midpoint of the interval above:
(59.9 + 40.7)/2 = 50.3
Standard deviation is the absolute value of the mean - endpoint
|59.9 - 50.3| = [B]9.6[/B]

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He r

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. The researcher posed a null hypothesis that the average weight for boys in that high school should be 100 lbs. What is the [B][U]absolute value[/U][/B] of calculated t that we use for testing the null hypothesis?
Mean is 109.4 and Standard Deviation = 20.79182532 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']statistics calculator[/URL]
Now use those values and calculate the t-value
Abs(t value) = (100 - 109.4)/ 20.79182532/sqrt(5)
Abs(tvalue) = [B]1.010928029[/B]

MAPE - MPE - MAPD

Given a time series of actual and forecasted values, this determines the following:

* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)

* Symmetric Mean Absolute Percentage Error (sMAPE)

* Mean Absolute Percentage Error (MPE)

* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)

* Symmetric Mean Absolute Percentage Error (sMAPE)

* Mean Absolute Percentage Error (MPE)

the absolute value of a number is its _____ from 0

the absolute value of a number is its _____ from 0
The answer is [B]distance[/B].
As an example: 2 and -2 are 2 units away from 0.

the absolute value of the difference 6 and k

the absolute value of the difference 6 and k
The difference of 6 and k means we subtract k from 6:
6 - k
Take the absolute value:
[B]|6 - k|[/B]

The distance between X and 8 is less than 14

Distance implies the positive difference between 2 points. Therefore, we use absolute value:
|x - 8| < 14
Note, we use less than since 14 is not included.

What numbers have an absolute value of 9

What numbers have an absolute value of 9
[LIST]
[*]9 since |9| = 9
[*]-9 since |-9| = 9
[/LIST]

which number is the same distance from 0 on the number line as 4

which number is the same distance from 0 on the number line as 4
We use absolute value for distance.
Since 4 is 4 units right of 0 on the number line, we can also move 4 units left of 0 on the number line and we land on [B]-4[/B]

“The shortest person in a class is 55 inches tall and tallest person in that class is 75 inches tall

The shortest person in a class is 55 inches tall and tallest person in that class is 75 inches tall. write an absolute value equation that requires the minimum and maximum height. Use X to represent heights.
We write our inequality as:
[B]55 <= X <= 75[/B]